SOLUTION: One of the same side angles of two parallel lines is five times smaller than the other one. Find all angles.

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Question 1102153: One of the same side angles of two parallel lines is five times smaller than the other one. Find all angles.
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13196)   (Show Source): You can put this solution on YOUR website!


Although you will see this kind of language used frequently, it has no meaning.

If one angle has measure x and the other has measure "5 times smaller than x", then the measure of the second angle is x, minus 5 times x, which is equal to -4x.

The measure of an angle formed by intersecting lines can't be negative.

And now that I read the problem more carefully, the statement of the problem is flawed in another way: two parallel lines don't form any angles....

Mathematics is "the exact science"; ambiguous or even meaningless language has no place in math.

Resubmit the problem with it stated correctly.

Or, if you have shown the problem exactly as it was given to you, then there is nothing you can do with it.
Answer by ikleyn(52756)   (Show Source): You can put this solution on YOUR website!
.
One of the same side angles of two parallel lines is five times smaller than the other one. Find all angles.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Sure, this formulation is incorrect.

The meaningful formulation might be this: 

    One of the two same side angles at two parallel lines and a transverse is one fifth of the other one. Find all angles.



Then the equation is 

x +  = 180 degs

 = 180  ====>  x =  = 150 degs.


Answer.  One angle is 150 degs, the other is 30 degs.

On parallel lines and the angles formed at a transverse line see the lesson
    - Parallel lines
    - HOW TO solve problems on parallel lines - Examples
in this site.

Also,  you have this free of charge online textbook on Geometry
    GEOMETRY - YOUR ONLINE TEXTBOOK
in this site.

The referred lesson is the part of this online textbook under the topic
"Basics of angles. Supplementary, complementary angles. Vertical angles. Parallel lines".

Save the link to this online textbook together with its description

Free of charge online textbook in GEOMETRY
https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson

to your archive and use it when it is needed.


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